Piecewise polynomial models for aggregation and regression analysis in remote sensing of the Earth problems

We discuss the procedures of data aggregation as a preprocessing stage for subsequent to regression modeling. An important feature of study is demonstration of the way how represent the aggregated data. It is proposed to use piecewise polynomial models, including spline aggregate functions. We show that the proposed approach to data aggregation can be interpreted as the frequency distribution. To study its properties density function concept is used. Applying data aggregation models as input and output variables we propose a new probability density function value linear regression model (Distributions Regression). To calculate the data aggregation and regression model we employ numerical probabilistic analysis (NPA). To demonstrate the degree of the correspondence of the proposed methods to reality, we developed a theoretical framework and considered numerical examples.